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Circuit analysis: Kirchhoff's laws

FIGURE 4 (in the attachment) shows two inductances connected in parallel across an a.c. supply.

(a) Apply Kirchhoff's voltage law to each loop of circuit.

(b) Hence or otherwise obtain the current ratio I1/I2 in terms of the circuit inductances.

(c) See if you can show that L1 and L2 can be replaced by the equivalent inductor of FIGURE 4.

(d) A 1 nF capacitor is placed across the two inductors (FIGURE 4 (c)). If L1 = L2 = L and k = 0.5, determine the required value of L if the minimum current I flows from the supply when it is at a frequency of 1 MHz.


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